Final Answer:
The geometric mean of x and z is found using (option A): √(x ⋅ z).
Step-by-step explanation:
The geometric mean is a mathematical concept used to find a measure of central tendency for a set of values, particularly when dealing with products. For two values, x and z, the geometric mean is determined by taking the square root of their product, as represented by option A: √(x ⋅ z). This calculation is based on the understanding that the geometric mean captures the multiplicative relationship between values (option A).
Option B, √(x + z), represents the square root of their sum, which is not the correct formula for the geometric mean. Similarly, option C, √(x / z), involves division, which is not the appropriate operation for calculating the geometric mean. Option D, √(x ⋅ y ⋅ z), introduces a variable y not present in the original question, making it an inaccurate choice.
In summary, the geometric mean, crucial in statistics and mathematics, is correctly determined for the legs x and z by taking the square root of their product, as given in option A. This choice reflects the essence of the geometric mean in capturing the scale of multiplicative relationships within a set of values, making it a valuable measure for various applications in data analysis and interpretation.